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The Star Garden
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Quantum Cloud by Antony Gormley
Wallace argued that we already use the concept of patterns to provide functional definitions and gives the example of our definition of a tiger. We can view the tiger from many perspectives and choose the one that is easier or most useful for us. We could, for example, try to learn about the behaviour of tigers by studying them at an atomic level but this would be overly complicated. We could study them at a cellular level, but again this would provide us with too much irrelevant information. We learn most about the behaviour of tigers by studying them in terms of single, individual tigers, patterns which arise from a background of energy and matter. Wallace claimed that we define a tiger as "any pattern which behaves as a tiger" (Wallace, 2003, pp.94).
In the case of Schrodinger's cat, the superpositional state of the inside of the box can be described as containing patterns of both a dead and alive cat as well as; "all possible macroscopic objects made out of the cat's subatomic constituents" (Wallace, 2003, pp.99). Cats are described as patterns and so cannot be in superpositions themselves, cats can only be duplicated. This level of description is not usually needed however, because decoherence will quickly remove all observable effects of the superposition.
Wallace agreed with American philosopher Daniel Dennett who claimed that a pattern is real if it is useful for us to refer to it when explaining theories (Dennett, pp.95-120). Usefulness is defined in terms of explanatory power and predictive reliability. Patterns are subjective just as worlds are and so it is possible that different minds perceive patterns, and hence define macroscopic objects, in different ways.
Pavement art by Julian Beever
References
Dennett, D., 1991, 'Real Patterns', Journal of Philosophy, Vol.87, pp.27-51, reprinted in Dennett, D., 1998, 'Brainchildren', MIT Press, Cambridge
Lewis, D., 1976, 'Survival and Identity', The Identities of Persons, Rorty, A.O. (ed.) University of California Press, California
Saunders, S., 1998, 'Time, Quantum Mechanics, and Probability', Synthese, Vol.114
Wallace, D., 2003, 'Everett and Structure', Studies In History and Philosophy of Science Part B: Studies In History and Philosophy of Modern Physics, Vol.34
Wallace, D., 2005a, 'Quantum Probability from Subjective Likelihood: improving on Deutsch's proof of the probability rule', Studies In History and Philosophy of Science Part B: Studies In History and Philosophy of Modern Physics, Vol.38, pp.311-332
Wallace, D., 2005b, 'Three kinds of branching universe', forthcoming
Wallace, D., 2006, 'Epistemology Quantized: circumstances in which we should come to believe in the Everett interpretation', British Journal for the Philosophy of Science, Vol.57
The Emerging Universe
English philosophers Simon Saunders (Saunders, pp.373-404) and David Wallace (Wallace, 2006, pp.655-689) argue that Lockwood is wrong to say that there is no answer to who we will become upon branching and suggested that we will become one particular mind after we branch in agreement with Albert and Loewer. An observer should expect to experience either one outcome or another after a quantum interaction and this creates an element of subjective indeterminacy. Saunders and Wallace accepted that this means we must have an infinite amount of minds inside of us at all times but did not agree with Albert and Loewer's dualist theory of the mind (Saunders, pp.390).
Wallace described how "when I say 'who will I become'" before initiating a quantum experiment with two possible results, "that statement should actually be ascribed to two versions of me" (Wallace, 2006, pp.669). We do not notice the fact that we have numerous minds because, from a subjective point of view, they will be indistinguishable, all seeing the same things and thinking the same thoughts at the same time. Saunders and Wallace advocated a Lewisian rather than Parfitian, notion of personal identity, this approach was suggested by American philosopher David Lewis in 1976 (Lewis, pp. 17-40).
Wallace argued that Lockwood's many minds approach is false because his interpretation of 'weight' does not make sense. There is no observable difference between worlds with a low or high weight and so pain will not be more intense in a world with higher weight. It also does not make sense to say that the pain will be experienced by a larger amount of minds because we always have at least an infinite amount of minds inside of us.
Wallace argued that Lockwood's many minds approach violates the functional definition of probability because it implies that it is logical to try to maximise the weight of the world we are in. This is impossible because branching occurs all the time and we have no way to keep track of this weight. Wallace described how it would lead to a person being "faced with the impossible task of calculating how much branching will occur across the entire lifetime of the Universe (contingent on his choice of action) in order to weigh up the value, now, to him of carrying out a certain act" (Wallace, 2005a, pp.331). If we do not care about our own weight then we should not care about the weights of our future-selves. Wallace argued that weights can only apply to events and not to people or worlds.
Wallace suggested that we can replace Lockwood's notion of a 'weighted branching universe' with that of an 'emergent branching universe'. Emergent branching universes can be thought of as an approximate description which emerges "from some underlying physical reality" where "there is no `finest-grained' structure of branches but only a vaguely-defined cut-off point below which `branching' talk ceases to be useful" (Wallace, 2005b, pp.20). An observer should be rationally compelled to act as if they are in a weighted branching universe, except for the fact that the concept of weight is meaningless when applied to people.
Wallace also argued that we do not need Lockwood's many minds approach in order to account for the preferred basis problem. He suggested that it does not matter that the basis of decoherence is approximate if you accept a functional definition of the mind (Wallace, 2003, pp.87-105). Wallace argued that all macroscopic objects should be understood "in terms of certain structures and patterns which emerge from quantum theory" (Wallace, 2003, pp.87).